The invention relates to digital data processing and, particularly, to registering 3D image volumes. The invention has application, by way of non-limiting example, in medical imaging, e.g., in aligning diagnostic images acquired by computed tomography (CT) and/or magnetic resonance imaging (MRI). Other applications include microscopy and geosciences, to name but a few fields.
A common problem in three-dimensional (3D) imaging is, given two different 3D image volumes of the same object or of two different but corresponding objects, to compute a 3D transformation (e.g., rotation, translation, scaling) that brings the two images into alignment, so that after transformation, corresponding points in the two images are coincident or at least close to each other. This problem arises, for example, in aligning multiple 3D images (e.g., of a patient's head) generated by Computed Tomography (CT) and/or Magnetic Resonance Imaging (MRI).
A widely accepted standard procedure for solving this problem is to search in a space of transformations for the transformation that maximizes the “mutual information” of the two images. (See, by way of non-limiting example, Viola, “Alignment by Maximization of Mutual Information,” PhD thesis, Massachusetts Institute of Technology (MIT), Cambridge, Mass., March 1995, also referred to as A.I. Technical Report No. 1548, dated June 1995, of the MIT Artificial Intelligence Laboratory, the teachings of which are incorporated herein by reference).
Thus, given two digital images A and B with range [0 . . . N−1], i.e.                A: 3→[0 . . . N−1], B: 3→[0 . . . N−1]        
then for a given transformation T: 3→3, the Mutual Information is defined by
      H    ⁡          (              A        ,                  B          ∘          T                    )        =      -                  ∑                  a          =          0                N            ⁢                          ⁢                        ∑                      b            =            0                    N                ⁢                                  ⁢                                            p                              A                ,                                  B                  ∘                  T                                                      ⁡                          (                              a                ,                b                            )                                ⁢                      log            ⁡                          (                                                p                                      A                    ,                                          B                      ∘                      T                                                                      ⁡                                  (                                      a                    ,                    b                                    )                                            )                                          
Here PA,B∘T(a,b) denotes the probability that a pixel value a in image A coincides with a pixel value b in the transformed image B∘T. In order to compute this probability, essentially a 2D histogram has to be computed, namely:
            p              A        ,                  B          ∘          T                      ⁡          (              a        ,        b            )        =            card      ⁡              (                  {                                                    x                ∈                G                            ❘                              A                ⁡                                  (                  x                  )                                                      =                                          a                ⋀                                  B                  ⁡                                      (                                          T                      ⁡                                              (                        x                        )                                                              )                                                              =              b                                }                )              ⁢          1              card        ⁢                                                  ⁢                                                ⁢        G            
Here card denotes the number of elements in a set. The set G of locations x over which the histogram is computed may be chosen to consist of all pixels centres of the reference image A, or of any other possibly smaller set of points.
With this background, an object of this invention is to provide improved methods and apparatus for digital data processing.
A more particular object, by way of example, is to provide improved methods and apparatus for registering 3D image volumes.
Yet another more particular object, again, by way of example, is to provide improved such methods and apparatus as can be implemented at lower cost. And, a related aspect of the invention is to provide such methods and apparatus as can be implemented using standard, off-the-shelf components.